ECB President Mario Draghi said the bank's policymakers discussed the possibility of cutting rates at their meeting on Aug. 2 "but the Governing Council in its entirety decided this was not the time".
A Reuters poll of economists conducted immediately after the Aug. 2 meeting pointed to a cut in the ECB's main refinancing rate to 0.5 percent in September from 0.75 percent, which is already a record low.
However, Draghi also tempered expectations of the ECB starting to charge banks for depositing funds with it overnight.
The ECB's overnight deposit rate, which it cut to zero on July 5, acts as a floor for money market rates as banks only lend to rival banks if they are able to earn a better rate of interest than at the central bank.
The ECB hopes the unprecedented move in the deposit rate to zero will nurture a return of more significant interbank lending by forcing banks to look for more profitable options.
Three-month Euribor rates, traditionally the main gauge of unsecured bank-to-bank lending, eased to 0.345 percent on Tuesday from 0.349 percent.
Six-month Euribor rates also fell, to 0.620 percent from 0.625 percent and shorter-term one-week rates inched down to 0.095 percent from 0.096 percent. Overnight rates fell to 0.112 percent from 0.115 percent.
Euribor rates, like their counterpart Libor bank-to-bank rates, are at the centre of a manipulation scandal after it emerged a number of banks were falsely submitting the Libor rates they pay.
Dollar-priced three-month bank-to-bank Euribor lending rates decreased to 0.777 percent from 0.784 percent, while overnight dollar rates were steady at 0.316 percent.
The ECB's move to stop paying interest on banks' deposits prompted them to make a stronger use of the current account facility, which still pays 0.75 percent interest for the required reserves.
A total of 326 billion euros was parked in the ECB's deposit facility overnight. Banks' current account deposits at the ECB dipped to 536 billion euros.
Euribor rates are fixed daily by the Banking Federation of the European Union (FBE) shortly after 0900 GMT.